1. Rasterization and Antialiasing
Angel & 7.12
Angel: Interactive Computer Graphics5E © Addison-Wesley 2009

2. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Objectives
Survey Line Drawing Algorithms
DDA
Bresenham
Antialiasing
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3. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Rasterization
Rasterization (scan conversion)
Determine which pixels that are inside primitive specified by a set of vertices
Produces a set of fragments
Fragments have a location (pixel location) and other attributes such color and texture coordinates that are determined by interpolating values at vertices
Pixel colors determined later using color, texture, and other vertex properties
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

4. Scan Conversion of Line Segments
Start with line segment in window coordinates with integer values for endpoints
Assume implementation has a write_pixel function
y = mx + h
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

5. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
DDA Algorithm
Digital Differential Analyzer
DDA was a mechanical device for numerical solution of differential equations
Line y=mx+ h satisfies differential equation
dy/dx = m = Dy/Dx = y2-y1/x2-x1
Along scan line Dx = 1
for(x=x1; x<=x2;x++) {
y+=m;
write_pixel(x, round(y), line_color) }
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

6. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Problem
DDA = for each x plot pixel at closest y
Problems for steep lines
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7. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Using Symmetry
Use for 1  m  0
For m > 1, swap role of x and y
For each y, plot closest x
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

8. Bresenham’s Algorithm
DDA requires one floating point addition per step
We can eliminate all fp through Bresenham’s algorithm
Consider only 1  m  0
Other cases by symmetry
Assume pixel centers are at half integers
If we start at a pixel that has been written, there are only two candidates for the next pixel to be written into the frame buffer
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9. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Candidate Pixels
1  m  0
candidates
last pixel -
Note that line could have
passed through any
part of this pixel
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10. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Decision Variable
d = Dx(b-a)
d is an integer
d > 0 use upper pixel
d < 0 use lower pixel
when Dx=1, d=b-a -
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11. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Incremental Form
More efficient if we look at dk, the value of the decision variable at x = k + ½
dk+1= dk +2Dy, if dk < 0
dk+1= dk +2(Dy-Dx), otherwise
For each x, we need do only an integer addition
and a test – a single instruction on graphics chips - - - -
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12. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Aliasing
Ideal rasterized line should be 1 pixel wide
Choosing best y for each x (or visa versa) produces aliased raster lines
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009

13. Antialiasing by Area Averaging
Color multiple pixels for each x depending on coverage by ideal line
antialiased
original
magnified
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14. Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009
Polygon Aliasing
Aliasing problems can be serious for polygons
Jaggedness of edges
Small polygons neglected
Need compositing so color
of one polygon does not
totally determine color of
pixel
All three polygons should contribute to color
Angel: Interactive Computer Graphics 5E © Addison-Wesley 2009